The key elements in the inequality are the amount of information
\(H[Y]\)  that informed traders have on the value \(Y\)  of the asset, the market temperature \(T\) 
and the expected gain \(\mathbb {E}[G]\)  of informed traders. The market
temperature \(T\)  measures the level of noise in the market. It
increases with the fraction of noise traders. It vanishes when these
are absent (\(\nu =1\) ) and it diverges when the fraction of informed
traders vanishes (\(\nu \rightarrow 0\) ). Therefore, (REF ) is very
similar to the bound for work extraction in information engines.
Interestingly, we find that the bound is attained asymptotically in the latter
limit, i.e. when \(T\rightarrow \infty \) . This is consistent with the fact that,
in this limit, the convergence of the price to the true value \(Y\)  and
the activity of informed traders is infinitely slow, as in a
quasi-static process in physics. In the analogy with physics,
gain extraction approximates a reversible process because at
infinite temperature thermalisation is infinitely fast. Interestingly,
reversibility is the condition that allows maximal work extraction,
as show in [1]}.
